Vaccination campaign impact

library(vaccinationimpact)

This package proposes to assess the impact of vaccination campaigns using the following methods:

Mathematical Formulas

1. Number of events averted by vaccination (NAE)

The number of events averted by vaccination at time \(t\) is calculated as:

\[NAE_t = e_{A(t)} \frac{VC_t VE_t}{(1 - VC_t VE_t)}\]

with:

2. Number of avertable events considering an increase in final coverage (NAbE)

The number of averted events with alpha parameter at time \(t\):

\[NAbE_t(\alpha) = e_{A(t)} \frac{VC(\alpha)_t VE_t}{(1 - VC(\alpha)_t VE_t)}\]

with:

\(VC(\alpha)_t\) is computed as:

\[VC_t(\alpha) = \sum_{i=1}^{t} (VC_t - VC_{t-1}) \left(1 + \frac{\alpha}{VC_T}\right)\]

with:

3. Number Needed to Vaccinate (NNV)

Machado et al. method

The number needed to vaccinate at time \(t\) is calculated as:

\[NNV_t = \frac{1}{R_{B(t)} VE_t}\]

where \[R_{B(t)} = \frac{e_{A(t)} + NAE_t}{N_t}\], \(R_{B(t)}\) represents the rate of events expected in a counterfactual population without a vaccination program

with:

  • \(VE_t\): Vaccine effectiveness at time \(t\)
  • \(e_{A(t)}\): Number of events at time \(t\)
  • \(NAE_t\): Number of events averted by vaccination at time \(t\)
  • \(N_t\): Population at risk at time \(t\)

Tuite and Fisman method

The number needed to vaccinate at time \(t\) is calculated as:

\[NNV_t = \frac{v_t}{NAE_t}\]

with:

  • \(v_t\): Number of vaccinated individuals at time \(t\)

Example

We use some toy data to illustrate the usage of the package: weekly coverage, incidence and vaccine effectiveness are provided in the package.

data(coverage_and_incidence_mock_data)
coverage <- coverage_and_incidence_mock_data$coverage_data
incidence <- coverage_and_incidence_mock_data$incidence_data

Coverage data:

The coverage values are computed considering a sample size of 1234 individuals.

head(coverage)
#>         week number_of_vaccinated weekly_coverage cumulative_coverage
#> 1 2023-10-01                   94      0.07617504          0.07617504
#> 2 2023-10-08                  154      0.12479741          0.20097245
#> 3 2023-10-15                  134      0.10858995          0.30956240
#> 4 2023-10-22                  143      0.11588331          0.42544571
#> 5 2023-10-29                  123      0.09967585          0.52512156
#> 6 2023-11-05                   69      0.05591572          0.58103728

Incidence data:

head(incidence)
#>         week events
#> 1 2023-10-01     45
#> 2 2023-10-08     56
#> 3 2023-10-15     48
#> 4 2023-10-22     49
#> 5 2023-10-29     42
#> 6 2023-11-05     35

Vaccine effectiveness data:

data(ve_mock_data)
head(ve_mock_data)
#>         week        ve
#> 1 2023-10-02 0.6344967
#> 2 2023-10-09 0.6493827
#> 3 2023-10-16 0.7369862
#> 4 2023-10-23 0.6604973
#> 5 2023-10-30 0.6610903
#> 6 2023-11-06 0.7377342

NAE

vaccine_effectiveness <- ve_mock_data$ve

nae <- compute_events_averted_by_vaccination(
  number_of_events = incidence$events,
  cumulative_coverage = coverage$cumulative_coverage,
  vaccine_effectiveness = vaccine_effectiveness
)
plot(nae, type = "l", xlab = "Time", ylab = "Events averted")

NAbE

nabe <- compute_events_avertable_by_increasing_coverage(
  number_of_events = incidence$events,
  cumulative_coverage = coverage$cumulative_coverage,
  vaccine_coverage_increase = 0.1, # 10% increase in final coverage
  vaccine_effectiveness = vaccine_effectiveness
)
plot(nabe$new_vaccine_coverage, type = "l", xlab = "Time", ylab = "Vaccine coverage with 10% increase")

plot(nabe$nabe, type = "l", xlab = "Time", ylab = "Events averted")

NNV

Machado et al. method

sample_size <- 1234

nnv <- compute_number_needed_to_vaccinate_machado(
  number_of_events = incidence$events,
  number_of_events_averted = nae,
  population_size = sample_size,
  vaccine_effectiveness = vaccine_effectiveness
)
nnv
#>  [1]  41.12997  29.50475  26.92473  27.41407  29.01461  27.30541  30.97586
#>  [8]  58.08314  60.58614  43.89116  93.86294 160.55538 137.54650 255.03374
#> [15] 230.88015 812.75083 511.59870 314.74289 351.58960 661.23225        NA
#> [22]        NA        NA        NA        NA        NA        NA        NA
#> [29]        NA        NA        NA        NA        NA        NA        NA
#> [36]        NA        NA        NA        NA        NA        NA        NA
#> [43]        NA        NA        NA        NA        NA        NA        NA
#> [50]        NA        NA        NA

Tuite and Fisman method

nnv <- compute_number_needed_to_vaccinate_tuite_fisman(
  number_of_vaccinated = cumsum(coverage$number_of_vaccinated),
  number_of_events_averted = nae
)
nnv
#>  [1]  41.12997  29.50475  26.92473  27.41407  29.01461  27.30541  30.97586
#>  [8]  58.08314  60.58614  43.89116  93.86294 160.55538 137.54650 255.03374
#> [15] 230.88015 812.75083 511.59870 314.74289 351.58960 661.23225        NA
#> [22]        NA        NA        NA        NA        NA        NA        NA
#> [29]        NA        NA        NA        NA        NA        NA        NA
#> [36]        NA        NA        NA        NA        NA        NA        NA
#> [43]        NA        NA        NA        NA        NA        NA        NA
#> [50]        NA        NA        NA

References

We applied an adapted version of methods used by Foppa et al. and Machado et al. for influenza vaccination impact.